SOLUTION OF INTEGRO-DIFFERENTIAL EQUATIONS USING INTEGRAL TRANSFORMATION TECHNIQUES

Abstract

This paper presents novel contributions to the theory and applications of integro-differential equations through advanced integral transformation techniques. We introduce new methodologies for solving linear and nonlinear integro-differential equations using modified Laplace transforms, Sumudu transforms, and Adomian decomposition methods. The research establishes convergence criteria for the proposed methods and demonstrates their effectiveness through numerical examples. Our findings reveal significant improvements in computational efficiency and accuracy compared to traditional approaches. The theoretical framework developed herein provides a foundation for future research in mathematical physics, engineering applications, and biological modeling. Keywords: Integro-differential equations, Laplace transform, Sumudu transform, Adomian decomposition, integral transformations, mathematical modeling.